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The approach that has generally been applied has been to choose a form for FA(a, 0), assume that the particle size distribution is independent of the spatial distribution, and adopt a functional form for each that is based either on convenience, on the results of dynamical calculations, or on other observational evidence, such as data from acoustic and penetration experiments or extrapolation of meteor fluxes. Models of the brightness and polarization of the zodiacal light are then computed and the model parameters adjusted until a fit with the observations is obtained. Even if a good fit is achieved, there is, of course, no guarantee that the model so obtained is unique, and a variety of models have been found to represent the data about equally well. Reviews of theoretical work have been given by Blackwell, Dewhirst, and Ingham (1967), Elsåsser (1963), and others.
The earliest models, which assumed an isotropic scattering function, made it necessary to postulate a high particle concentration near the Sun to account for the steep increase in brightness in the F corona. Allen (1946) and van de Hulst (1947) independently showed that the brightness distribution in the F corona can be accounted for by diffraction without having to assume large numbers of dust particles close to the Sun. Ingham (1961) and Blackwell, Ingham, and Petford (1967) also treated the scattering function as a diffraction component plus a reflection component in deriving the albedo and the spatial distribution from coronal observations. Separating the scattering function into reflection and diffraction components is valid at all scattering angles for particles much larger than the wavelength. At small scattering angles, the diffraction component will be adequate for spherical particles a few micrometers in size at optical wavelengths. Diffraction will predict too steep a rise in intensity in the forward direction for particles less than 1 pum in size. (See van de Hulst, 1957, and Giese, 1961.)
With the introduction of high-speed computers, many authors have generated models using Mie theory to compute the scattering functions. The most extensive calculations have been carried out by Giese (1961), Giese and Siedentopf (1962), Giese (1963), and Giese and Dziembowski (1967). Similar studies have been done by Little, O'Mara, and Aller (1965); Elsåsser and Schmidt (1966); Aller et al. (1967); Powell et al. (1967); and Hanner (1970).
COMPARISON OF THEORY AND OBSERVATION
Most of the observations available for comparison with theoretical models are restricted to the ecliptic plane. Even here there are wide discrepancies among the results of different observers, due in part to the difficulties in correcting for atmospheric scattering and in separating the zodiacal light from the airglow and integrated starlight. These problems have been discussed by Weinberg (1970). The most extensive published data on the distribution of the zodiacal light brightness away from the ecliptic are by Smith, Roach, and Owen (1965). Their observations were made at only one wavelength, so that models that fit their data at 530 nm cannot be tested over a wide wavelength range. Ingham and Jameson (1968) and Jameson (1970) observed the brightness and polarization at 510 nm in regions away from the ecliptic.
Model calculations indicate that the polarization is a more sensitive discriminant than the intensity in determining the optical properties and size distribution of the dust particles. The maximum observed polarization Pinax in the ecliptic (about 23 percent at 530 nm) occurs near e = 70° (Weinberg, 1964). For a reasonably smooth spatial distribution, regardless of the exact form, a maximum near e = 70° implies a maximum polarization at scattering angles near 90°. On the basis of Mie theory, the maximum polarization occurs near 6 = 90° (and thus e = 70°) only if a significant number of particles have radii on the order of 0.1 pum or less. This is true for both dielectric and metallic particles. For n(a) or a-P this means p > 4 and als O.1 um. When the particle size distribution is weighted toward larger radii, Mie theory predicts the following changes:
(1) Metals: Pmax shifts to smaller scattering angles (0 × 90°).
(2) Ices (m - 1.3): Pinax shifts to larger angles (6 - 130° to 150°).
(3) Silicates (1.5 s m s 1.75): Large amounts of negative polarization occur over a wide range of scattering angles.
Thus, a fit to the observed polarization in the ecliptic plane with a single-component model requires that the scattering particles be predominantly of radius a 3.0.1 p.m. Both Giese and Dziembowski (1967) and Aller et al. (1967) found that the single-component model (m = 1.3) giving the best fit to the intensity and polarization in the ecliptic did not match the data of Smith, Roach, and Owen away from the ecliptic. Giese and Dziembowski proposed a two-component model consisting of silicates and iron particles, n(a) or a-2-3. By adjusting the cutoff sizes and the relative concentration of the two components, they were able to produce a polarization maximum near 70° and to improve the fit to the observed brightness perpendicular to the ecliptic. The presence of negative polarization near the antisolar direction has been discussed by Weinberg and Mann (1968). They find that the polarization reversal occurs near e = 165° at 508 nm and shifts toward smaller elongation at longer wavelength. Mie theory predicts negative polarization at large scattering angles for dielectric particles less than 1 um in size consisting of either ices of silicates. The negative polarization extends over a wider range of scattering angles at larger refractive index. For refractive index m = 1.3, the appropriate choice of size and spatial distribution can produce a neutral point near e = 165° at 508 nm. However, for a power-law size distribution, the position of the neutral point shifts to larger e at longer wavelength. The published observational data have limited coverage in both space and time as well as a limited range in wavelength. In spite of the amount of effort that has been expended in analyzing these observations, very few definitive conclusions can be drawn regarding the physical nature of the dust particles. On the theoretical side, too much emphasis has been placed on adjusting mathematical parameters to fit a specific idealized model to a limited set of observations. We must take a broader approach and ask what qualitative features can be used to discriminate between different kinds of scattering particles and what observational data will be most valuable for this purpose.
The wavelength dependence of polarization is a critical parameter in determining the size range and physical nature of the dust particles. More extensive data are needed from a good ground-based site, covering the entire sky over a wide range of wavelengths.
Ground-based observations have several limitations, however. Corrections for tropospheric scattering and airglow emission are uncertain. The ultraviolet and infrared spectral regions cannot be observed. Observations outside of eclipse are restricted to e > 30°. Figure 2 shows the region of space sampled by the line of sight for a series of elongation angles. It can be seen that at e = 30° we can get no information about the region closer than 0.5 AU to the Sun. It is therefore important to obtain detailed observations from satellites to supplement the ground-based data. The following types of observations are of particular value.
Observations in the Ultraviolet
The scattering properties of small particles depend on the quantity 2ma/A. Thus in the ultraviolet the particles “look” larger, and a better discrimination between different size distributions will be possible. We would expect the I, (e) curve to have a steeper slope in the ultraviolet at e <90° and the position of maximum in the PA(e) curve to shift. Assuming Mie theory provides at least a qualitative indication of the particle scattering properties, we expect the maximum polarization to shift toward larger e if the particles are dielectric (ices or silicates) and toward smaller e if the particles are metallic. The two-component model of Giese and Dziembowski would show a broadened maximum or perhaps a double maximum. Negative polarization may appear either at small angles or near the backscatter direction depending on the particle sizes and refractive index. The larger as A also means that effects of shape and surface irregularities will show up more strongly in the ultraviolet.
More fundamentally, many materials have a change in their optical properties in the ultraviolet region (Taft and Philipp, 1965; Field, Partridge, and Sobel, 1967). Thus it is important to search for “signatures” of certain materials by studying the wavelength variation of the intensity and polarization in the ultraviolet. The interstellar extinction curve, for example, shows a bump near 220 nm (Stecher, 1965). The presence of unusual features in the zodiacal light at 220 nm could have interesting implications in relating the interplanetary and interstellar grains.
Observations at Small Elongations
The importance of relating observations of the F corona and the zodiacal light has been stressed by van de Hulst (1947), Blackwell and Ingham (1967), and many others. Observations of the F corona made during eclipse are difficult to relate to zodiacal light data, for almost no data exist in the intervening region. The region at small e is critical for several reasons:
(1) The change in slope of IA(e) with A (5°se < 50°) provides
Simultaneous Satellite and Ground-Based Observations
The large body of ground-based data would become more valuable if accurate methods of correcting for tropospheric scattering and airglow emission can be developed. Simultaneous observations from the ground and from a satellite using similar instruments and wavelength bands can provide direct information on the effects of Earth's atmosphere. Such observations should be carried out over an extended period of time so that effects of variation in airglow emission and possible variations in the zodiacal light can be evaluated.
Observations in the infrared at small e can provide information on the thermal properties of the dust particles and the extent of the dust-free zone surrounding the Sun (Peterson, 1963, 1964; Harwit, 1963). Eclipse observations at 2.2 and 3.5 pum have been obtained by Peterson and MacQueen (1967) that show a maximum at 4.0 and a secondary peak at 3.5 solar radii (distance from the center of the Sun). Satellite data can provide more extensive coverage in space and time.
SCATTERING BY IRREGULAR PARTICLES
Many of the theoretical models of the zodiacal light brightness and polarization used to draw conclusions concerning the particle size distribution and composition have been based on the scattering functions for smooth, homogeneous, spherical particles, whereas the dust particles gathered in collection experiments are generally irregular, even fluffy in appearance (Hemenway et al., 1967; Hemenway and Hallgren, 1970; Hemenway et al., 1970). The assumption is implicitly made that an extended size distribution of randomly oriented, irregular particles will scatter light in the same manner as the same size distribution of spheres. There are little experimental data available for particles of size at-X with which to test the validity of this assumption.
Donn and Powell (1962) have studied the scattering by a size distribution of zinc oxide crystals, m = 2.01, which grow in the form of spikes. They found that the scattering characteristics for a size distribution of such particles could be represented by a distribution of much smaller spheres with m = 2.01 or moderately smaller spheres with refractive index as low as 1.2. Their work and other research on irregular particles have been summarized by Powell et al. (1967), who conclude that the scattering by a size distribution of large-volume particles such as cubes can be described by a size distribution of spheres very close to the real size distribution. They find that the angular dependence of the intensity and polarization at different wavelengths can be duplicated by the same distribution of spheres. For small-volume particles such as needles and fourlings, the equivalent size distribution of spheres that matches their data at